A washing machine rests on spring mounts. During the spin cycle, the wet clothes in the rotating drum are not evenly distributed, so the drum exerts a periodic force on the machine. The frequency of this force is equal to the rotation frequency of the drum.
The machine and its contents can be modelled as a mass–spring system oscillating vertically. The mounts obey Hooke's law.
Explain what is meant by resonance.
The mass of the empty washing machine is 72 kg. When wet clothes of mass 8.0 kg are placed in the drum, the machine sinks a further 2.0 mm on its mounts.
Calculate the rotation rate of the drum, in revolutions per minute, at which resonance occurs.
During the spin cycle, the drum accelerates from rest to a maximum rotation rate of 1200 revolutions per minute.
The machine vibrates violently, but only for a short time while the drum is speeding up.
Suggest why the machine vibrates violently only for a short time.
The spring mounts are replaced with mounts containing oil. This increases the damping of the oscillations.
Explain the effect of this change on the amplitude of the oscillations at resonance.
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